| Abstract: | 在此研究計畫中, 我們針對Greene (2005) 的真固定效果長期追蹤調查資料隨機邊界模型 (true-fixed effect panel stochastic frontier model), 提出當該模型殘差項具自我迴歸特性時的估計方式。此模型有兩大特點:(1) 模型中同時包含了固定個體效果及隨時間變動的無效率效果(time-varying inefficiency effects), 亦即Greene (2005) 的基本模型形式。以往文獻中, 往往因為incidental parameters 的問題及估計方法上的困難, 使此二效果無法同時存在, 影響實證應用上的可行性。Chen et al. (2011) 則是利用封閉型偏常態(closed skew normal; CSN) 分配對該模型提出具一致性的估計式。本研究計畫即是在Chen et al. 的基礎上發展而來。(2) 模型中的自我迴歸乃是定義在模型整體殘差項, .it = vit ? uit, 之上, 而非如以往文獻, 侷限在單一的uit 之上。固然uit 代表的無效率可能因為廠商無法迅速的調整生產效率而產生自我相關, 但vit 代表的外生衝擊亦可能因為具有持續性而造成自我相關。因此, 兩者的可能性皆不應被忽略。由於此類模型的意義, 主要是在於探討當資料存在自我相關特性時, 如何得出具一致性的模型參數估計, 因此我們將把重點放在模型整體殘差(.it) 的自我相關, 而不細究其來源。在估計方法上, 我們將延續Chen et al. (2011) 的方法, 利用CSN 分配的特性協助估計式的推導。
In this research project, we will propose a consistent estimator for true-fixed effect panel stochastic frontier model with autoregressive errors. There are two important characteristics of this model: (1) The model is based on Greene’s (2005) specification which includes both of the fixed individual effect and the inefficiency effect in the model. Prior to Greene’s specification, the literature would have only one of the two effects, but not both. The inability to adopt the more flexible specification may be due to the difficulty in estimating such a model where the incidental parameters problem presents. Chen et al. (2011) used properties of the closed skew normal (CSN) distribution to overcome the estimation problem, and we will adopt the similar estimation strategy in this research. (2) The autoregression is defined on the composed error of the model, i.e., .it = vit ?uit, rather than on only uit as the existing literature has done. Although uit could be serially correlated due to the slow adjustment of firm’s efficiency level, the serial correlation could also arise in vit if the exogenous shocks are correlated. Therefore, ignoring either source of the correlation may be shortsighted. Since the purpose of the correlation adjustment is to improve estimation efficiency and/or obtain consistent estimates, in this research we will focus on the model’s autoregressive error but not the exact source of it. |
